Economics Letters 124 (2014) 446–448
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Economics Letters journal homepage: www.elsevier.com/locate/ecolet
On the value of relative comparisons in firms Abhijit Ramalingam ∗ School of Economics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
highlights • • • • •
In a principal–agent setting, we explore heterogeneous relative concerns of agents. We find that firms may not always benefit from such heterogeneity. They only benefit when the difference outweighs the difference in agents’ abilities. We next account for the influence of other co-workers on agents’ relative concerns. Now, firms make lower profits relative to the no-comparisons benchmark.
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Article history: Received 23 April 2014 Received in revised form 29 June 2014 Accepted 11 July 2014 Available online 17 July 2014
abstract In a principal–agent model, we find that firms may not always benefit from the relative concerns of agents if such concerns are heterogeneous. Further, accounting for the influence of the environment on such concerns, profits are reduced relative to the no-comparisons benchmark. © 2014 The Author. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
JEL classification: D86 L14 M52 Keywords: Comparisons Incentives Context-dependence Profits
If status is to play a role in economic behavior, then, the benefit of status in economic environments must be explored. [— Ball and Eckel 1998, p. 501.] 1. Introduction There is little doubt that status or relative concerns affect agents’ choices and behavior. Such influence in firms and markets was first documented by Duesenberry (1949) and Leibenstein (1950) and more recently by Frank (1985), Ball and Eckel (1998) and Ball et al. (2001), to name a few. Previous work has found that firms benefit from the presence of status-minded employees. For instance, Fershtman et al. (2006), Frey (2007) and Besley and Ghatak (2008) find that employees motivated by relative comparisons require lower monetary incentives for effort.
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Previous work has mostly focused on symmetric agents in firms, i.e., all agents display the same intensity of concern for relative comparisons. An exception is Fershtman et al. (2006) who consider agents who either care about status or do not. However, agents are still one of the two extreme types. Another plausible situation is one where agents care about comparisons but to varying degrees. In such situations, we find that firms may not always benefit from the relative concerns of their employees. Firms only make higher profits when differences in relative concerns outweigh the difference in abilities between agents. To see if such a situation is likely, we relax another common assumption — that agents care about comparisons to the same degree with all co-workers. There is growing evidence that ‘‘players’ regard for one another may depend on who the opponent is’’ (Levine, 1998, p. 598) and that such regard is shaped by the institutions and culture in which agents interact (Bowles, 1998). Using the framework of Raub (1990), environmental features have been shown to influence the level of altruism (Rotemberg, 1994),
http://dx.doi.org/10.1016/j.econlet.2014.07.013 0165-1765/© 2014 The Author. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3. 0/).
A. Ramalingam / Economics Letters 124 (2014) 446–448
trust (Casadesus-Masanell, 2004) and work ethic (Ramalingam and Rauh, 2010) in agency relationships. Following the approach of Casadesus-Masanell (2004), we explore such ‘‘context-dependence’’ of agents’ relative concerns in the firm. We find that it is only the less able agents who care about comparisons and work harder, a prediction that is supported by empirical evidence. However, this negatively impacts firm profits relative to a situation when no agent cares about comparisons.
We consider a moral-hazard model with one principal and two agents (Fershtman et al., 2006). Agents produce observable outputs of identical commodities, qi , which are non-deterministic functions of effort, ei : i = 1, 2,
(1) 1
where E[ϵi ] = 0. We assume linear wage schemes :
wi = αi + βi qi , i = 1, 2, (2) where αi is a fixed salary and βi is the bonus or incentive
component.2 It is easy to see that agents whose outputs depend on each other might care about relative concerns. We explore if relative concerns play a role even when there are no technological interdependencies in production, i.e., ∂ qi /∂ qj = 0. The expected profit of the riskneutral principal is given by
Π = e1 − (α1 + β1 e1 ) + e2 − (α2 + β2 e2 ).
(3)
In addition to standard payoffs, we assume that agents also care about relative performance.3 The expected utility of risk-neutral agent i is given by4 Ui = αi + βi ei −
take-it-or-leave-it contract offers,5 (iii) if agents accept, efforts and outputs are realized. We solve the game by backward induction using standard techniques (Bolton and Dewatripont, 2005) and proofs are omitted. Agents’ chosen efforts from stage (iii) and the contract parameters from stage (ii) are6 ei = (βi + δi )/ki
and
βi = 1 − δj ,
i = 1, 2, i ̸= j.
(5)
2.1. Benchmark — no relative concerns
2. A model of relative concerns
qi = ei + ϵi ,
447
ki e2i
+ δi (ei − ej ), i = 1, 2, i ̸= j, (4) 2 where δi ∈ R+ is the importance agent i attaches to comparisons and 21 ki e2i (ki > 0) is agent i’s cost of effort. Reservation utility, U¯ i , is normalized to zero. We assume that k1 ≥ k2 , i.e., agent 2 is more able than agent 1. We allow for heterogeneous relative concerns, i.e., δ1 ̸= δ2 . Following Rotemberg (1994), we term an agent’s utility as defined above as ‘‘behavior payoffs’’ and his utility when δi = 0 (the standard case) his ‘‘material payoffs’’. This distinction between the ‘‘acting self’’ and ‘‘object self’’ in economics goes back to at least Akerlof (1983) and Rabin (1993). Context-dependence is captured by modeling the intensity of relative comparisons, δi , as being chosen to maximize agent i’s material payoffs within the environment, here the firm (Raub, 1990). Following CasadesusMasanell (2004), we model the choice as one by agents themselves. Rotemberg (1994) argues that an individual’s ‘‘inner self’’ is motivated by material payoffs but can shape behavior payoffs that determine the actions of the ‘‘outer self’’. For our purposes, it is not important that agents choose δi . They could instead be a result of parents choosing values for their children (Akerlof, 1983) or ‘‘behavioral conditioning’’ by society (Bernheim, 1994) to maximize chances of economic success in the workplace. It is only important that the choice is made prior to the interaction and that agents commit to their choices (Frank, 1987). The timing in the game is: (i) agents simultaneously choose δi and δj , (ii) the principal observes behavior payoffs and makes
1 While the linear contract is generally suboptimal, Bose et al. (2011) provide a strong empirical justification for its use in this standard case. 2 Our results hold if wages depend on the other agent’s output. 3 See, for instance, Azmat and Iriberri (2010) on the impact of relative performance information on effort. 4 All results remain unchanged if we instead assume negative exponential utility.
In the benchmark case with no relative concerns (δi = δj = 0), the principal offers ‘‘selling-the-store’’ contracts, i.e., βiB = 1. Individual efforts and the total effort in the benchmark equilibrium case are given by eBi = 1/ki
and
eB ≡ eB1 + eB2 =
k1 + k2
.
k1 k2 Agents’ wages and the firm’s total wage bill are
wiB = 1/2ki and wB ≡ w1B + w2B =
k1 + k2 2k1 k2
(6)
(7)
and firm profits are
ΠB =
k1 + k2 2k1 k2
.
(8)
2.2. Heterogeneous relative concerns When δi , δj > 0, individual effort and the wage bill are
ei =
1 + δi − δj
and w =
(k1 + k2 )[1 − (δ1 − δ2 )2 ]
ki and firm profits are
= Π
2k1 k2
k1 (1 − δ1 + δ2 )2 + k2 (1 + δ1 − δ2 )2 2k1 k2
> 0.
(9)
(10)
While the firm’s wage bill goes down ( w − w B < 0), it is not clear what happens to the total effort in the firm; effort increases for the agent who has stronger relative concerns while it decreases for the other agent. As a result, the effect on profits is not clear,
− Π B ≥ 0 ⇔ δ1 − δ2 ≥ Π
2(k1 − k2 ) k1 + k2
(≥ 0).
(11)
Proposition 1. With heterogeneous relative concerns, firms only gain if the difference in agents’ relative concerns outweighs the difference in their abilities. Utility from favorable comparisons can provide some compensation for agents’ effort costs. Condition (11) stipulates that agents’ increase in utility from concerns is large enough to compensate for the greater share of the effort cost (from k1 and k2 ) borne by the agents due to reduced wages. That is, firms can gain only if relative concerns are strong enough to not cause a significant reduction in effort despite the reduction in wages. Note that if k1 = k2 , the firm gains only if agents have heterogeneous relative concerns. 2.3. Context dependent relative concerns Given the participation constraint, agent i’s material utility can be written as −δi (ei − ej ). Simultaneous maximization in stage (i) yields
δ1∗ =
k1 − k2 2(k1 + k2 )
> 0 and δ2∗ = 0.
5 We assume that the principal has all the bargaining power. 6 The first-order approach is valid.
(12)
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A. Ramalingam / Economics Letters 124 (2014) 446–448
Proposition 2. The less able agent cares about relative comparisons while the more able agent does not. Note that if k1 = k2 , δ1 = δ2 = 0. Corollary 1. If agents are of the same ability, neither agent cares about relative comparisons. Incentives, individual efforts and wages in the equilibrium are given by
β1∗ = 1 = β1B and β2∗ = e∗1 =
3k1 + k2 2k1 (k1 + k2 )
w1∗ = w2∗ =
(k1 + 3k2 ) 2k2 (k1 + k2 )
> eB1 and e∗2 =
2k31 + k1 k2 (7k1 + 4k2 ) + 3k32 8k1 k2 (k1 + k2 )2
(k1 + 3k2 )
2
8k2 (k1 + k2 )2
< 1 = β2B
k1 + 3k2 2k2 (k1 + k2 )
(13)
< eB2
(14)
> w1B and (15)
< w2B .
(k1 + k2 )2 + 12k1 k2 > 0. 8k1 k2 (k1 + k2 )
(16)
At the equilibrium, (11) is not satisfied. Thus, firm profits are reduced in equilibrium,
Π∗ − ΠB = −
3(k1 − k2 )2 8k1 k2 (k1 + k2 )
< 0.
(17)
Proposition 3. With context-dependent relative concerns, profits are reduced relative to the no-comparisons benchmark. Relative to the benchmark, incentives are weaker for the more able agent while they are unchanged for the less able agent. Thus, only the less productive agent (agent 1) works harder in the equilibrium due to the additional motivation through relative comparisons. This finding is supported by evidence from the laboratory and the field. Falk and Ichino (2006) find that less productive experimental subjects work harder while more productive ones either reduce or do not change their efforts. Mas and Moretti (2009) find a similar effect among supermarket checkout clerks. As a result, the principal pays the less able agent a higher wage while reducing the wage of the more able agent. While the principal saves on the wage bill, total effort is also reduced relative to the benchmark. e∗ − eB = −
(k1 − k2 )2
